The invention is in the field of seismic surveys useful in exploring for valuable subsurface resources. One aspect of the invention concerns vertical seismic profiling and more particularly separating the compressional and shear components of the vector wavefield measured in vertical seismic profiling. Another aspect concerns similar separation in surface seismics (also called horizontal profiling).
Vertical seismic profiling, often abbreviated as VSP, is a technique in which a seismic signal generated at or near the surface of the earth is recorded by geophones secured at various depths to the wall of a borehole. Unlike the more commonly used horizontal seismic profiling, where the geophones are strung along the earth surface, vertical seismic profiling uses geophones at locations spaced along the borehole axis. These geophones typically respond to both upgoing and downgoing seismic events, in contrast to horizontal seismic profiling, where the geophones typically cannot respond directly to downgoing events. The distance between geophone recording locations in vertical seismic profiling is typically a small fraction of that used in horizontal profiling.
Vertical seismic profiling measurements can give insight into some fundamental properties of propagating seismic waves and assist in the structural, stratigraphic, and lithological interpretation of subsurface formations. For example, an important use of VSP measurements is to help define upgoing and downgoing seismic events within the earth and thereby help determine which events arriving at the surface are primary reflections and which are multiples. Other applications of VSP include estimation of reflector dip, correlation of shear wave reflections with compressional wave reflections, location of fault planes, determination of lithological effects on propagating wavelets, looking for reflectors ahead of the drill bit, determining hydrocarbon effects on propagating wavelets, identification of intrabed multiples, measurement of both compressional and shear wave velocities, and estimation of the conversion of compressional to shear and shear to compressional energy modes within the earth. Background information concerning VSP can be found in Hardage, B.A., Vertical Seismic Profiling, Part A: Principles, Geophysical Press, 1983, Volume 14A of Handbook Of Geophysical Exploration, Section I. Seismic Exploration, Helbig and Treitel (Editors); Society of Exploration Geophysics, Expanded Abstracts of the Technical Program With Authors' Biographies, Sept. 11-15, 1983, Las Vegas, Nev., pp. 522- 540; Wuenschel, P.C., The Vertical Array In Reflection Seismology--Some Experimental Studies, Geophysics, Volume 41, No. 2 (Apr. 1976), pp. 219-232; and U.S. Pat. Nos. 4,383,308 and 4,563,757.
As discussed in greater detail in these background documents, which are hereby incorporated by reference, in principle vertical seismic profiling involves providing a seismic source at or near the earth surface and near a borehole, and providing vertical seismic profile measurements by means of geophones positioned at selected depth levels in the borehole. While it should be possible to position geophones at each desired depth in the borehole such that all can respond to the same seismic event generated by the source, it is believed typical, at least in the Western world, to use instead a geophone (or geophones) carried by a single seismic tool which is suspended by cable in the borehole and is successively clamped to the borehole wall at selected depths, to thereby respond to different wavelets from the source at different depths. Various kinds of seismic sources can be used, and typically it is desirable that the source produce a consistent and repeatable shot wavelet, particularly when a single downhole geophone tool is used. For example, the source can be a small chemical explosive shot near the bottom of a relatively shallow, cased and cemented well drilled near the borehole, or it can be one of the impulsive surface sources, such as weight droppers and devices that use explosive gases or compressed air to drive a heavy pad vertically downward with great force, or vibrators of the kind used as energy sources in hydrocarbon exploration. The borehole can be vertical or deviated, so long as the deviation is accounted for in interpreting the measurements, and can be cased or uncased. A typical downhole tool used in vertical seismic profiling typically contains at least one geophone that is sufficiently protected to withstand the adverse environment in a deep borehole and yet can achieve satisfactory acoustic coupling with the formation. Two typical configurations are a tool that has a retractable electrically operated pivot arm which can press the geophone(s) against the borehole wall at selected depth levels, and a tool with a retractable electrically driven telescoping ram serving the same purpose. The geophone transducer element or elements in a VSP tool can be either only vertically oriented or can be, for example, in a 3-component orientation (e.g., orthogonal at xyz or tilted relative to each other at some other angle, e.g., at 54.degree.). In 3-component xyz geometry, the geophone along the z (depth) axis in a vertical borehole measures vertical particle motion, and the geophones oriented along the x and y directions measure particle motion along two orthogonal directions in the horizontal plane. Typically the three geophones are designed to exhibit closely matched amplitude and phase responses, and the device that presses the tool against the borehole wall is designed to create a geophone-to-formation bond which would result in the horizontal geophones being mechanically coupled to the formation in the same way as the vertical geophone. A 3-component tool typically also includes an orientation measuring device (typically made up of one or more magnetometers that measure azimuth from magnetic North and one or more gravity sensitive accelerometers that measure deviation from vertical), a downhole digitizing system which can digitize the geophone transducer outputs within the tool and send the digitized signals up to the surface through wires in the cable suspending the tool, and other equipment, such as devices to check the quality of acoustic coupling with the formation. Known processing equipment and techniques can be used at the surface to record the tool outputs and make preliminary corrections, such as for tool orientations, to thereby produce vector measurements which can be designated u (x=0,z,t). Each such measurement can be a digitized vector set identifying the direction in space and the magnitude of the seismic energy measured by the 3-component VSP tool at the borehole (x=0) at depth z for each sample time t over a selected time interval. See U.S. Pat. No. 4,563,757.
Typically the output of any given geophone contains contribution from both compressional and shear wave components (and may contain contributions from other wave components) even when the surface seismic source is designed to optimize the generation of compressional and minimize the generation of shear waves. Even if the surface source could generate a purely compressional wave, a considerable amount of compressional wave energy may still be converted into shear wave modes whenever a propagating compressional wave encounters a reflecting surface at an oblique angle of incidence. It is believed that these converted shear wave modes can be valuable for interpreting subsurface geological conditions, as can be shear modes deliberately created by shear wave energy sources. For example, converted shear wave modes can be particularly valuable seismic measurements when used in concert with compressional wave energy measurements to interpret elastic constants of rocks or to predict the types of pore fluids in rock units or to predict other subsurface lithology parameters. In addition, certain techniques can benefit from such separation because they need, or are believed to work better with, direct or indirect measurements of only the compressional, or only the shear components of the total energy arriving at downhole geophones. One example is the use of a technique similar to medical computed tomography and relying on offset VSP, or on well-to-well VSP measurements to image the zx plane of interest. Such a technique is helped by the use of data representing the separated compressional (or perhaps shear) component of the total energy measured at the downhole geophones. In surface seismics, typically it is assumed that the geophones measure primarily the compressional component of the arriving seismic energy, and it is believed that typically little or no effort is made to separate the shear component contributions and thereby improve the results of processes based on compressional wave considerations.
For these and other reasons, proposals have been made in the past to separate the compressional and shear wave components of the seismic energy measured at a VSP geophone. For example, the Hardage document cited earlier proposes, e.g. at page 413, that with a 3-component tool the responses of the triaxial geophone system can be mathematically rotated so that they represent the output of a single geophone oriented along the ray path of the compressional wave first arrival at each recording level, and that data can be derived which represent the response that a geophone would record if it were positioned in a vertical plane containing the compressional wave first arrival ray path and then oriented in this plane so that it is normal to the compressional wave ray path, and that these data thus would contain the full response of those downgoing shear velocity modes which travel along the same ray path as the compressional wave direct arrival, partial responses of SV modes which arrive at the triaxial geophone arrangement along ray paths that differ from the compressional wave ray path, and partial responses of later arriving downgoing or upgoing compressional wave events whose ray paths intersect the geophone assembly at various angles of inclination. The earlier cited document concerning the technical program of Sept. 11-15 1983 in Las Vegas, Nev. proposes, e.g. at page 522, that for processing VSP data from compressional wave or shear wave sources, the apparent velocity between recording positions can be used to separate upgoing and downgoing waves, and that similarly, the P, SV, and SH modes for the direct arrival in a VSP can be isolated, based on their orthogonal polarization, but reports that both techniques break down when analyzing complex wave types such as converted waves. The same document proposes at pages 524-527 a technique which involves considering the first compressional (P) ray as included in the source-well plane, deriving a projection along the first arriving P ray, which should give mainly the first arriving P ray and following multiples, deriving a projection which is normal to that first arriving P ray and is in the source-well plane, which should give direct and converted shear SV waves, and deriving a projection normal to the source-well plane, which should give shear SH waves. The Hardage document cited earlier observes, e.g. at pages 177 and 178, that when VSP measurements taken in the space-time domain are converted to the frequency-wavenumber domain, a masking function could be superimposed over the VSP data in the frequency-wavenumber domain in order to suppress events not travelling with compressional velocity, and gives a conceptual illustration at FIG. 5-20 of a so-called pie slice velocity band pass masking function which would reduce the magnitudes of all energy modes except the upgoing compressional reflections. Other types of frequency-wavenumber velocity filtering are also discussed in the Hardage document, e.g. at pages 174-176.
It is believed that said earlier separation proposals can give useful results when the subsurface environment is relatively simple, e.g., when it can be expected that compressional and direct and converted shear modes would not arrive at a given geophone location at the same time. However, in practice the typical environment can be sufficiently complex to defeat such velocity or polarization separation techniques. Therefore, it is believed that a need remains for accurately and efficiently separating the compressional and shear wave components in seismic profiling, and it is this need that the invention seeks to meet.
The invention makes use of the unexpected discovery that, if certain assumptions are made about the properties of the geological formation and the wavefield, and some knowledge available from VSP and/or other logs is used, it is possible to relate the compressional wave component to the total measured wave vector through an analytical expression which can be sufficiently accurate to give useful results. The assumptions believed most important are that the subsurface formation is locally homogeneous (for example, over intervals of at least about 3 wavelengths) in the region of measurements, and that the elastic wavefield is approximately constant in the direction normal to the plane containing the source and the borehole. The knowledge derived from VSP and/or other logs (e.g., sonic) can comprise the local compressional and shear velocities and/or the local slowness, such as the local slowness of waves in the vector wavefield. Because of the assumption that the formations adjacent the borehole are locally isotropic, there is only a single inherent P or S velocity for a given depth, and it can be assumed to be that measured by a sonic logging tool or by a zero-offset VSP. In principle, the main steps of an embodiment of the invention are to decompose the 3-component measurements into local plane wave components, identify the P and S waves of each plane wave component by polarization, and separately recombine the so-identified P and S waves.
In a particular and nonlimiting example, the sought compressional component is related to the total measured wavefield vector through a transfer function (filter) in matrix form which depends on local acoustic properties of the formation, and hence typically changes with borehole depths. These local properties are measured or deduced beforehand, for example by VSP and/or compressional and shear sonic well logging. As a specific example, the variations of compressional velocity and shear velocity with borehole depth are measured, e.g. by compressional wave source and by shear wave source sonic logging, and the results are used to produce a 2-dimensional matrix filter. VSP (vertical seismic profiling) is then used to measure the vector wavefield for each depth level of interest, e.g. with a 3-component tool. After any preliminary processing of the VSP measurements (e.g. to account for tool orientation and seismic energy attenuation), a subset made up of measurements within a given window in borehole depth and in time is forward Fourier transformed, for example by a commercially available FFT processor, to convert it to measurements in a corresponding window in wavenumber-frequency space. The resulting subset of converted measurements is then combined, for example in a dot product operation, with the transfer function (filter) for the borehole depth interval in that window. The result is subjected to inverse Fourier transformation, for example again by means of a commercially available FFT processor, to thereby derive a vector quantity representative of the compressional wave vector at the given borehole depth. Vector subtraction of this compressional wave vector from the total measured vector wavefield for that depth gives a vector quantity representative of the shear wave vector component at the same given borehole depth. The procedure is repeated for other depth levels. In a second exemplary embodiment, the corresponding steps can be carried out entirely in the spatial domain, without excursions into wavenumber-frequency space, to give corresponding end results.
In the embodiments described above the process can be thought of as a multi-channel (vertical and horizontal particle motion), multi-dimensional (time and depth) filtering operation. The required filters have impulse responses which are both spatially and temporally infinite, or at least seek to approximate such responses within practical constraints, despite the fact that actual recordings of measurements are far from being infinite in extent. However, it has been discovered that overall accuracy can suffer significantly when the vertical spatial extent of the seismic measurements is severely limited, for example because measurements are not taken for all depths of interest, or because the approximations of constant velocity are only valid over a severely limited vertical interval. One practical example where this can occur is when very thin beds are encountered in the subsurface formations of interest. Usually, no difficulties are encountered with respect to the effort to approximate the effect of filter with a temporally infinite impulse response, because the VSP measurements are or can be taken over a sufficiently long time period and sampled at a suitable rate. These considerations have led to the discovery of a third implementation of the invention, which works particularly well in cases where the first and second embodiments may give less accurate results, and also works well in cases in which the nature of the original measurements and of the subsurface formations allow for the fully successful use of the first and second embodiments. In this third implementation, filters with a spatially finite impulse response are used on measurements from a finite depth interval; however, the frequency-wavenumber response of such filters can only approximate the desired frequency-wavenumber response. Often, much of the energy of the measurements is concentrated along a few rays in frequency-wavenumber space, corresponding to a small number of apparent (vertical) velocities. In accordance with the third implementation of the invention, the frequency-wavenumber response of the finite length filters can be made to coincide with the desired response on these rays, to minimize the error in the reconstructed compressional and shear waves. However, to do this, separate filters are required for the respective depth points in the borehole; the resulting collection of filters can be thought of as a single shift-varying filter. The original measurements can be analyzed to determine the predominant apparent velocities for the respective depth levels, and the separation can be done using shift-varying filters designed to minimize error at these velocities.
In an exemplary and nonlimiting embodiment of the third implementation of the invention, the VSP traces for the horizontal and vertical components of the wavefield for the respective depth points in the borehole are transformed in time, into the space-frequency domain. In that domain, they are filtered at each temporal frequency independently. The samples of the reconstructed compressional wave are produced in that space, and are inverse-transformed (in time) to obtain the reconstructed P-component time waveform. The reconstructed compressional component is subtracted from the starting waveform to obtain the reconstructed shear component time waveform. Advantage can be taken of the fact that the starting and reconstructed waveforms must be realvalued, to perform the intermediate processing (filtering) only on the temporal transform values for positive frequencies. The requisite filter can be derived, in accordance with one example of the invention, from the original VSP measurements.
In the first embodiment of the invention a double Fourier transformation of the VSP measurements is used, from the space-time to the wavenumber-frequency space, and the filtering is done in wavenumber-frequency space and the result is double transformed back to the space-time domain. In the second embodiment, the equivalent operations are carried out entirely in the space-time domain. In contrast, in the third embodiment, only a single (temporal) Fourier transformation is used, the filtering is performed in the space-frequency domain, and the result is inverse-transformed back to the space-time domain through a single (temporal) inverse Fourier transformation.
The invented principles, while described in detail only for VSP separation, apply to surface seismics separation as well.